The system of equations we have is
[tex]\mleft\{\begin{aligned}-1+y=0 \\ 2+7x=-8y\end{aligned}\mright.[/tex]Now, to find the aumented matrix, we have to have all of the variables in each equation on one side, for this in the first equation we add 1 to both sides of the equation:
[tex]\begin{gathered} -1+y=0 \\ -1+1+y=0 \\ y=1 \end{gathered}[/tex]And for the second equation we need to add 8y to both sides and substract 2 from both sides (this is to have variables on the left and independent number on the right):
[tex]\begin{gathered} 2+7x=-8y \\ 7x+8y=-2 \end{gathered}[/tex]Now, the system is left as follows
[tex]\mleft\{\begin{aligned}y=1 \\ 7x+8y=-2\end{aligned}\mright.[/tex]We represent this a matrix with the following form:
The first line will represent the first equation
The second line will represent the second equation
And the first column will be the x values, and the second column the y values:
[tex]\begin{bmatrix}{0} & {1} & {1} \\ {7} & {8} & {-2}{}\end{bmatrix}[/tex]I will expand on the meaning of this in the following diagram:
That last one is the aumented matrix of the system.
